Antireflection coating, optical element, optical system and optical apparatus

ABSTRACT

The antireflection coating is a multi-layer film to be formed on a surface of a substrate. The film includes multiple layers including an uppermost layer most distant from the substrate among the multiple layers, and a lower layer including at least one layer other than the uppermost layer. A refractive index nm of the uppermost layer for a wavelength of λ (nm) satisfies a condition of 1.11≤nm≤1.3. An optical admittance Y of the lower layer is expressed by Y=a+ib, and a and b in the optical admittance satisfy conditions of (a−1.13)2+(b−0.24)2≤0.452 for λ=430, (a−1.33)2+(b+0.05)2≤0.252 for λ=900 and (a−1.14)2+(b+0.25)2≤0.292 for λ=1800.

BACKGROUND OF THE INVENTION

Field of the Invention

The present invention relates to an antireflection coating formed by amulti-layer film.

Description of the Related Art

Optical apparatuses such as surveillance cameras include ones requiredto be capable of not only visible light image capturing, but alsonear-infrared light image capturing in darkness such as night. Suchimage capturing in darkness is made possible using airglow radiated dueto a chemical reaction and an electromagnetic reaction in theatmosphere. The airglow, which is generated in a wavelength range from avisible range to a near-infrared range, has a peak in a wavelength rangefrom 1450 nm to 1800 nm in the near-infrared range (see “Seeing Photons:Progress and Limits of Visible and Infrared Sensor Arrays” (Committee onDevelopments in Detector Technologies; National Research Council, 2010)pp. 25).

On the other hand, a surface of a light-transmissive member such as alens used in an image capturing optical system is provided with, inorder to reduce a reflectance thereat, an antireflection coating formedby a multi-layer film in which multiple dielectric thin films formed byevaporation (deposition) are layered. Furthermore, an antireflectioncoating including an uppermost layer whose material has a lowerrefractive index than a refractive index of 1.38 of magnesium fluorideused for the evaporated film can provide a higher antireflectionperformance. As low refractive index materials, inorganic materials suchas silica and magnesium fluoride and organic materials such as siliconresin and non-crystalline fluorine resin are known. These materials canreduce their refractive indices by forming voids in their layers.

In the optical apparatuses capable of the visible light image capturingand the near-infrared light image capturing, a reduction of thereflectance of the light-transmissive member such as the lens not onlyreduces a generation of unwanted light such as flare and ghost, but alsoincreases an amount of transmitted light to obtain more imageinformation.

Japanese Patent Laid-Open No. 2013-250295 discloses an antireflectioncoating having an antireflection effect from the visible range to thenear-infrared range. This antireflection coating has a twelve-layerstructure in which high refractive index films and low refractive indexfilms are alternately layered, and its twelfth layer as an uppermostlayer is formed of an extremely low refractive index material whoserefractive index is in a range from 1.20 to 1.29.

However, the antireflection coating disclosed in Japanese PatentLaid-Open No. 2013-250295 has a reflectance characteristic that itsreflectance increases in a wavelength range of 1600 nm or more and thatprovides a reflectance of 1% or more in a wavelength range near 1700 nm.Since the airglow has its peak in the wavelength from 1450 nm to 1800 nmas described above, a level of an antireflection performanceapproximately the same as that of the antireflection coating disclosedin Japanese Patent Laid-Open No. 2013-250295 is insufficient for theairglow.

SUMMARY OF THE INVENTION

The present invention provides an antireflection coating having a highantireflection performance in a wide wavelength range from 430 nm to1800 nm in which not only visible light but also airglow can be used.The present invention further provides an optical element provided withthe antireflection coating, an optical system and an optical apparatus.

The present invention provides as an aspect thereof an antireflectioncoating as a multi-layer film to be formed on a surface of a substrate.The coating includes multiple layers including an uppermost layer mostdistant from the substrate among the multiple layers, and a lower layerincluding at least one layer other than the uppermost layer. Arefractive index n_(m) of the uppermost layer for a wavelength of A (nm)satisfies a condition of 1.11≤n_(m)≤1.3. An optical admittance Y of thelower layer is expressed by Y=a+ib, and a and b in the opticaladmittance satisfy conditions of (a−1.13)²+(b−0.24)²≤0.45² for λ=430,(a−1.33)²+(b+0.05)²≤0.25² for λ=900 and (a−1.14)²+(b+0.25)²≤0.29² forλ=1800.

The present invention provides as other aspects thereof an opticalelement, an optical system and an optical apparatus using the aboveantireflection coating.

Further features and aspects of the present invention will becomeapparent from the following description of exemplary embodiments withreference to the attached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a sectional view of an antireflection coating that is arepresentative embodiment of the present invention.

FIGS. 2A to 2C describes equivalent optical admittances of thin filmlayers in the embodiment.

FIG. 3 illustrates an optical admittance of Embodiment 1 in a complexcoordinate system.

FIG. 4 illustrates a reflectance characteristic of an antireflectioncoating of Embodiment 1.

FIG. 5 illustrates optical admittances of lower layers of antireflectioncoatings of Embodiments 2 to 4 in the complex coordinate system.

FIG. 6 illustrates optical admittances of lower layers of antireflectioncoatings of Embodiments 5 to 7 in the complex coordinate system.

FIG. 7 illustrates a reflectance characteristic of the antireflectioncoating of Embodiment 2.

FIG. 8 illustrates a reflectance characteristic of the antireflectioncoating of Embodiment 3.

FIG. 9 illustrates a reflectance characteristic of the antireflectioncoating of Embodiment 4.

FIG. 10 illustrates a reflectance characteristic of the antireflectioncoating of Embodiment 5.

FIG. 11 illustrates a reflectance characteristic of the antireflectioncoating of Embodiment 6.

FIG. 12 illustrates a reflectance characteristic of the antireflectioncoating of Embodiment 7.

FIG. 13 illustrates optical admittances of lower layers ofantireflection coatings of Embodiments 8 to 64 for λ=430 nm in thecomplex coordinate system.

FIG. 14 illustrates optical admittances of lower layers ofantireflection coatings of Embodiments 8 to 64 for λ=900 nm in thecomplex coordinate system.

FIG. 15 illustrates optical admittances of lower layers ofantireflection coatings of Embodiments 8 to 64 for λ=1800 nm in thecomplex coordinate system.

FIG. 16 illustrates reflectance characteristics of the antireflectioncoatings of Embodiments 8 to 64 for an incident angle of 0 degree.

FIG. 17 illustrates reflectance characteristics of the antireflectioncoatings of Embodiments 8 to 64 for an incident angle of 45 degree.

FIG. 18 is a perspective view of an optical apparatus that is Embodiment65.

DESCRIPTION OF THE EMBODIMENTS

Exemplary embodiments of the present invention will hereinafter bedescribed with reference to the accompanying drawings.

FIG. 1 illustrates a structure of an antireflection coating (film) 10formed as a multi-layer film, which is a representative embodiment ofthe present invention. The antireflection coating 10 is provided on anoptical element such as a lens. The antireflection coating 10 isprovided on a surface of a substrate 0 that is a body (optical elementbody such as a lens portion that is a light-transmissive portion) of theoptical element. The antireflection coating 10 is a multi-layer filmincluding two or more layers. Specifically, the antireflection coating10 includes a lower layer 11 and an uppermost layer m; the lower layer11 includes a first thin layer 1 to an (m−1)-th thin layer m−1, and theuppermost layer m is an m-th layer. The uppermost layer m is a layermost distant from the substrate 0 and is a most-surface-side layerforming a boundary with air. The uppermost layer m has a refractiveindex from 1.10 to 1.30 for a wavelength λ (430≤λ≤1800) (nm), which is alower refractive index layer than those of the thin film layers 1 tom−1.

According to the following reference literature, using an opticaladmittance and a characteristic matrix enables a thin film design inwhich two boundaries that are one between an entrance medium and a thinfilm and one between that thin film and a substrate are converted intoone boundary expressed by an equivalent optical admittance.

REFERENCE LITERATURE

-   Cheng-Chung Lee, “Optical thin films and film-forming techniques”,    Agne gijutsu center Inc.

The optical admittance is a ratio of an electric field intensity and amagnetic field intensity in a medium. When Y0=√(ε0/μ0) that is a valuein vacuum is used as a unit, the optical admittance can be considered asbeing equivalent to a refractive index of the medium.

Description will be made of a case where, as a structure illustrated inFIG. 2A, a ray vertically reaches a boundary r₀₋₁ between the substrate0 and the thin film (first thin layer) 1 and a boundary r₁₋₂ between thethin film layer 1 and the thin film layer 2. An electric field intensityand a magnetic field intensity at the boundary r₀₋₁ are respectivelyrepresented by Et and Ht, and an electric field intensity and a magneticfield intensity at the boundary r₁₋₂ are respectively represented by Eiand Hi.

Since the optical admittance of the thin film layer 1 is equivalent to arefractive index n₁ of the thin film layer 1, Et, Ht, Ei and Hi at theboundaries r₀₋₁ and r₁₋₂ has a relation expressed by followingexpression (1).

$\begin{matrix}{\begin{bmatrix}{Ei} \\{Hi}\end{bmatrix} = {\begin{bmatrix}{\cos\;\delta_{1}} & {\frac{i}{n_{1}}\sin\;\delta_{1}} \\{{in}_{1}\sin\;\delta_{1}} & {\cos\;\delta_{1}}\end{bmatrix}\begin{bmatrix}{Et} \\{Ht}\end{bmatrix}}} & (1)\end{matrix}$

A phase difference δ₁ of the thin film layer 1 is expressed as followswhere d₁ represents a film thickness of the thin film layer 1 and n₁represents the refractive index of the thin film layer 1 for awavelength λ of an incident light.δ₁=2πn ₁ d ₁/λ  (2)

Expression (1) is rewritten as following expression (3) using an opticaladmittance Yt=Et/Ht=n_(s) of the substrate 0.

$\begin{matrix}{\begin{bmatrix}B_{1} \\C_{1}\end{bmatrix} = {\begin{bmatrix}{\cos\;\delta_{1}} & {\frac{i}{n_{1}}\sin\;\delta_{1}} \\{{in}_{1}\sin\;\delta_{1}} & {\cos\;\delta_{1}}\end{bmatrix}\begin{bmatrix}1 \\{Yt}\end{bmatrix}}} & (3)\end{matrix}$

When Y₁=C₁/B₁, Y₁ is an equivalent optical admittance of the substrate 0and the thin film layer 1, which is calculated from the boundaries r₀₋₁and r₁₋₂ and the thin film layer 1. That is, the structure illustratedin FIG. 2A is equivalent to a structure illustrated in FIG. 2B, so thatthe substrate 0 and the thin film layer 1 can be considered as a virtuallayer 010 having an equivalent refractive index Y₁. Repeating thisprocedure (m−1) times makes it possible to simply express the substrate0 and the lower layer 11 (1 to m−1) in the structure in FIG. 2A as avirtual layer 100 having an equivalent optical admittance Y_(m-1) asillustrated in FIG. 2C. The equivalent optical admittance Y_(m-1) isexpressed by following expression (4) using refractive indices n_(j)(j=1 to m−1) and phase differences δ_(j) (j=1 to m−1) of the thin filmlayers including the lower layer 11:

$\begin{matrix}{\begin{bmatrix}B_{m - 1} \\C_{m - 1}\end{bmatrix} = {{\underset{j = 1}{\overset{m - 1}{\Pi}}\begin{bmatrix}{\cos\;\delta_{j}} & {\frac{i}{n_{j}}\sin\;\delta_{j}} \\{{in}_{j}\sin\;\delta_{j}} & {\cos\;\delta_{j}}\end{bmatrix}}\begin{bmatrix}1 \\{Yt}\end{bmatrix}}} & (4)\end{matrix}$where Y_(m-1)=C_(m-1)/B_(m-1).

On the other hand, from expression (4), an equivalent optical admittanceY_(m)=C_(m)/B_(m) from the substrate 0 to the uppermost layer m isexpressed by following expression (5).

$\begin{matrix}{\begin{bmatrix}B_{m} \\C_{m}\end{bmatrix} = {\begin{bmatrix}{\cos\;\delta_{m}} & {\frac{i}{n_{m}}\sin\;\delta_{m}} \\{{in}_{m}\sin\;\delta_{m}} & {\cos\;\delta_{m}}\end{bmatrix}\begin{bmatrix}1 \\Y_{m - 1}\end{bmatrix}}} & (5)\end{matrix}$

A refractive index of air is 1, and a reflectance at the boundarybetween the uppermost layer m and the air is 0 when Y_(m) is as follows.Y _(m) =C _(m) /B _(m)=1  (6)

The equivalent optical admittance Y_(m-1) for the wavelength λ of theincident light (the wavelength λ is hereinafter referred to as “anincident wavelength”) is expressed in complex notation as follows:Y _(m-1)(λ)=a+ib.

In this case, when the reflectance at the boundary between the uppermostlayer m and the air is 0, a locus of complex coordinates (a, b) becomes,from expressions (5) and (6), a circle whose center is located at((n_(m) ²+1)/2, 0) and whose radius is (n_(m) ²−1)/2. A position (point)of the complex coordinates (a, b) is uniquely specified from theincident wavelength λ and the film thickness d_(m) of the uppermostlayer m. For example, when the uppermost layer m has a refractive indexof 1.25, the locus of complex coordinates (a, b) becomes a circle whosecenter is located at (1.28, 0) and whose radius id 0.28. In order toreduce a reflectance of the antireflection coating 10 to near 0%, it isonly necessary to form the lower layer 11 such that the complexcoordinates (a, b) on that circle is close to a point uniquely specifiedby the incident wavelength λ and the film thickness d_(m) of theuppermost layer m.

The antireflection coating 10 of this embodiment is characterized inhaving a high antireflection performance in a wavelength range from 430nm to 1800 nm in which not only visible light but also airglow can beused. In order to achieve this characteristic, the complex coordinates(a, b) of the equivalent optical admittance from the substrate 0 to thelower layer 11 (the equivalent optical admittance is hereinafter simplyreferred to as “an optical admittance of the lower layer 11”) satisfythe following conditions.(a−1.13)²+(b−0.24)²≤0.45² for λ=430  (7)(a−1.33)²+(b+0.05)²≤0.25² for λ=900  (8)(a−1.14)²+(b+0.25)²≤0.29² for λ=1800  (9)

As described above, when the complex coordinates (a, b) are located nearthe point uniquely specified, on the above-described circle, by theincident wavelength λ and the refractive index n_(m) and the filmthickness d_(m) of the uppermost layer m, the reflectance is reduced.Therefore, it is simply only necessary to form the lower layer 11 suchthat, in the wavelength range from 430 nm to 1800 nm, the complexcoordinates (a, b) are located near the uniquely specified point on thecircle. However, materials used for the lower layer 11 are limited inreality, so that it is difficult to realize a film structure of thelower layer 11 such that, in the wide wavelength range from 430 nm to1800 nm, the complex coordinates (a, b) are located near the uniquelyspecified point on the circle.

On the other hand, using a film structure satisfying the conditions ofexpressions (7), (8) and (9) enables forming such a lower layer 11 usinggeneral materials, which achieves a low reflectance in the widewavelength range from 430 nm to 1800 nm.

It is more desirable that the complex coordinates (a, b) of the opticaladmittance of the lower layer 11 satisfy the following conditions.(a−1.10)²+(b−0.22)²≤0.26² for λ=430  (10)(a−1.33)²+(b+0.05)²≤0.20² for λ=900  (11)(a−1.18)²+(b+0.26)²≤0.25² for λ=1800  (12)

It is further desirable that the complex coordinates (a, b) of theoptical admittance of the lower layer 11 satisfy at least one of thefollowing conditions in the wavelength range of 430≤λ≤1800:(a−1.09)²+(b−0.20)²≤0.35²  (13)(a−1.28)² +b ²≤0.35²  (14)(a−1.27)²+(b+0.28)²≤0.35²  (15)

It is desirable that the film thickness d_(m) (nm) of the uppermostlayer m satisfy the following condition.125n _(m) ×d _(m)≤250  (16)

In general, an optical film thickness of a thin film on a substratecorresponding to a quarter of an incident wavelength λ makes itsreflectance minimum.

In the embodiment, in a case where the wavelength range is a wide rangefrom 430 nm to 1800 nm, when a vicinity of an inverse of an intermediatepoint of an inverse of this wavelength range is four times of theoptical film thickness, a low reflectance is provided.

Furthermore, it is desirable that the antireflection coating 10 have,for a ray in the wavelength range from 430 nm to 1800 nm, a reflectanceof 1.5% or less when an incident angle of the ray is 0° or more and 15°or less and have a reflectance of 4.5% or less when the incident angleis 30° or more and 45° or less.

Moreover, it is desirable that a number of layers of the antireflectioncoating 10 (total layer number of the lower layer 11 and the uppermostlayer m) be nine or more. This is because a smaller total layer numberthan nine makes it difficult to improve the antireflection performance.

In addition, when, among materials of (two or more layers of) the lowerlayer 11, a highest refractive index material has a refractive indexrepresented by n_(H), and a lowest refractive index material has arefractive index represented by n_(L), it is desirable that n_(H) andn_(L) satisfy the following condition.0.4≤n _(H) −n _(L)≤0.9  (17)

This is because a large difference between the refractive indices ofthese materials makes it easy to achieve a low reflectance in a widewavelength range.

The uppermost layer m is formed of a low refractive index materialincluded in inorganic materials and organic materials. Such lowrefractive index inorganic materials include oxide silicon such assilica (Sio₂) and magnesium fluoride (MgF₂), and such low refractiveindex organic materials include silicon resin and non-crystallinefluorine resin. The uppermost layer m includes voids thereinside. Air(whose refractive index is 1.0) contained in the voids reduces therefractive index of the uppermost layer m. In addition, the uppermostlayer m is desirable to be a film formed by binding hollow fineparticles or solid fine particles with a binder. These fine particlesare desirable in order to reduce the refractive index to be chieflyformed of a low reflectance material such as Sio₂ or MgF₂.

On the other hand, the lower layer 11 is desirable to be formed of anyone of oxides of titanium, tantalum, zirconia, chromium, niobium,cerium, hafnium, aluminium, silicon and yttrium, or a mixture thereof.The thin film layer 1 as the first layer of the lower layer 11 isdesirable in order to prevent white opaque and others to be formed ofAl₂O₃, SiN_(x), SiON or Nb₂O₅.

The uppermost layer m formed by binding the fine particles with thebinder is desirable to be formed by, as a film forming method, a sol-gelmethod. A coating method for the uppermost layer m is not limited to aparticular one, that is, common coating methods for coating with coatingliquids can be used such as a dip coating method, a spin coating method,a spray coating method and a roll coating method. From a viewpoint ofenabling forming a film whose film thickness is uniform on the substrate0 such as a lens having a curved surface, the spin coating method isdesirable to be used.

After the coating, the uppermost layer m is dried using a dryer, a hotplate, an electric furnace or the like. The drying is performed underconditions of temperature and time that do not influence the substrate 0and that can evaporate organic solvent inside and between the fineparticles. In general, it is desirable to use a temperature of 300° C.or less. A number of times of the coating is normally desirable to beone, but the coating and the drying may be repeated multiple times.

The lower layer 11 is desirable in order to simplify film formation tobe formed by a dry method such as a vacuum evaporation method or asputtering method.

Next, specific embodiments will be described. These embodiments aremerely examples, and thus embodiments of the present invention are notlimited thereto.

Embodiments 1 to 7

An antireflection coating 10 of each of Embodiments 1 to 7 is formed asa multi-layer film including thirteen layers. In Embodiments 1 to 7, thesubstrates 0 have mutually different refractive indices, but materialsof thin films forming the antireflection coatings 10 are mutuallyidentical.

Table 1 shows film structures of Embodiments 1 to 7. First to twelfthlayers constitute a lower layer 11, which are formed on a substrate 0 bya vacuum evaporation method.

An uppermost layer as a thirteenth layer is formed by performing coatingwith a coating liquid, which is produced by adding a binder to asolution containing hollow SiO₂ fine particles and mixing them, with aspin coater and then performing burning for one hour in a clean ovenwhose temperature is from 100 to 250° C.

The uppermost layer thus formed is adjusted such that, in all ofEmbodiments 1 to 7, its refractive index for a d-line (587.6 nm) is 1.25and its film thickness is 145 nm.

FIG. 3 illustrates an optical admittance of the lower layer 11 (that is,an equivalent optical admittance from the substrate 0 to the lower layer11) in Embodiment 1 in a complex coordinate system.

A horizontal axis indicates a real part a of Y=a+ib, and a vertical axisindicates an imaginary part b thereof. The upper limit of the conditionof expression (7) is illustrated by a short broken line circle, theupper limit of the condition of expression (8) is illustrated by adashed-dotted line circle, and the upper limit of the condition ofexpression (9) is illustrated by a long broken line circle. Opticaladmittances (complex coordinates) inside these circles satisfy thecorresponding conditions. This also applies to other embodimentsdescribed later.

Furthermore, a locus of complex coordinates of the optical admittancewhen an incident wavelength λ is from 430 nm to 1800 nm is illustratedby a solid line. Complex coordinates for λ=430 nm are illustrated by ablack rectangle, complex coordinates for λ=900 nm are illustrated by ablack triangle, and complex coordinates for λ=1800 nm is illustrated bya black circle (point).

As understood from FIG. 3, the optical admittances of the lower layer 11in Embodiment 1 for λ=430 nm, 900 nm and 1800 nm satisfy the conditionsof expressions (7), (8) and (9).

FIG. 4 illustrates reflectances in a wavelength range from 430 to 1800nm in Embodiment 1. A reflectance for an incident angle of 0 degree(vertical incidence) is illustrated by a solid line, a reflectance foran incident angle of 15 degrees is illustrated by a dotted line, areflectance for an incident angle of 30 degrees is illustrated by abroken line, and a reflectance for an incident angle of 45 degrees isillustrated by a dashed-dotted line. As understood from FIG. 4, in thewavelength range from 430 to 1800 nm, the reflectances in Embodiment 1are 1.5% or less for the incident angles of 0 and 15 degrees and 4.5% orless for the incident angles of 30 and 45 degrees, which provides a highantireflection performance.

FIG. 5 illustrates optical admittances of the lower layers 11 inEmbodiments 2, 3 and 4 in the complex coordinate system. Loci of complexcoordinates of the optical admittances when the incident wavelength λ isfrom 430 nm to 1800 nm in Embodiments 2, 3 and 4 are illustratedrespectively by a solid line, a short broken line and a long brokenline. Complex coordinates for λ=430 nm in Embodiments 2, 3 and 4 areillustrated respectively by a black rectangle, a white rectangle and agray rectangle. Complex coordinates for λ=900 nm in Embodiments 2, 3 and4 are illustrated respectively by a black triangle, a whit triangle anda gray triangle. Complex coordinates for λ=1800 nm in Embodiments 2, 3and 4 are illustrated respectively by a black circle, a whit circle anda gray circle.

FIG. 6 illustrates optical admittances of the lower layers 11 inEmbodiments 5, 6 and 7 in the complex coordinate system. Loci of complexcoordinates of the optical admittances when the incident wavelength λ isfrom 430 nm to 1800 nm in Embodiments 5, 6 and 7 are illustratedrespectively by a solid line, a short dashed line and a long dashedline. Complex coordinates for λ=430 nm in Embodiments 5, 6 and 7 areillustrated respectively by a black rectangle, a white rectangle and agray rectangle. Complex coordinates for λ=900 nm in Embodiments 5, 6 and7 are illustrated respectively by a black triangle, a whit triangle anda gray triangle. Complex coordinates for λ=1800 nm in Embodiments 5, 6and 7 are illustrated respectively by a black circle, a whit circle anda gray circle.

As understood from FIGS. 5 and 6, the optical admittances of the lowerlayer 11 in Embodiments 2 to 7 for λ=430 nm, 900 nm and 1800 nm satisfythe conditions of expressions (7), (8) and (9).

FIGS. 7 to 12 illustrate reflectances in the wavelength range from 430to 1800 nm in Embodiments 2 to 7. In each drawing, a reflectance for theincident angle of 0 degree is illustrated by a solid line, a reflectancefor the incident angle of 15 degrees is illustrated by a dotted line, areflectance for the incident angle of 30 degrees is illustrated by abroken line, and a reflectance for the incident angle of 45 degrees isillustrated by a dashed-dotted line. As understood from FIGS. 7 to 12,in the wavelength range from 430 to 1800 nm, the reflectances in each ofEmbodiments 2 to 7 are 1.5% or less for the incident angles of 0 and 15degrees and 4.5% or less for the incident angles of 30 and 45 degrees,which provides a high antireflection performance.

TABLE 1 Refractive Embodiment Layer Material index 1 2 3 4 5 6 7 13thHollow 1.25 Physical 145.0 145.0 145.0 145.0 145.0 145.0 145.0 SiO₂ Film12th Ta₂O₅ 2.30 Thickness 7.0 4.3 5.4 2.7 2.4 2.0 5.0 11th SiO₂ 1.46(nm) 81.7 96.6 95.0 111.4 117.2 120.5 101.3 10th Ta₂O₅ 2.30 20.2 21.323.2 20.7 20.5 19.6 21.9 9th SiO₂ 1.46 33.8 37.4 37.2 41.4 42.8 43.742.6 8th Ta₂O₅ 2.30 34.9 43.1 45.8 41.7 42.2 41.6 42.9 7th SiO₂ 1.4612.4 11.4 10.1 13.7 13.7 14.4 15.3 6th Ta₂O₅ 2.30 161.9 172.1 175.0170.0 168.4 172.0 188.3 5th SiO₂ 1.46 14.5 16.9 17.3 15.0 13.6 12.2 8.94th Ta₂O₅ 2.30 42.1 37.1 40.2 42.2 44.8 49.2 54.9 3rd SiO₂ 1.46 35.037.3 35.5 29.2 26.0 22.5 16.3 2nd Ta₂O₅ 2.30 20.2 17.2 19.4 20.0 27.134.7 40.1 1st Al₂O₃ 1.63 119.6 116.7 15.0 4.6 12.8 14.7 10.0 SubstrateRefractive 1.50 1.60 1.70 1.80 1.90 2.00 2.10 index

Embodiments 8 to 64

Tables 2 to 10 show film structures of Embodiments 8 to 64. In each ofEmbodiments 8 to 64, a lower layer 11 other than an uppermost layer isformed on a substrate 0 by a vacuum evaporation method. The uppermostlayer is formed by performing coating with a coating liquid, which isproduced by adding a binder to a solution containing hollow SiO₂ fineparticles and mixing them, with a spin coater and then performingburning for one hour in a clean oven whose temperature is from 100 to250° C.

FIG. 13 illustrates optical admittances of the lower layers 11 (each ofwhich is an equivalent optical admittance from the substrate 0 to thelower layer 11) in Embodiments 8 to 64 for an incident wavelength λ=430nm in a complex coordinate system. A horizontal axis indicates a realpart a of Y=a+ib, and a vertical axis indicates an imaginary part bthereof. This also applies to complex coordinate systems illustrated inother drawings described later. The upper limit of the condition ofexpression (7) is illustrated by a short broken line circle. Asunderstood from FIG. 13, the optical admittances of the lower layers 11in Embodiments 8 to 64 for λ=430 nm satisfy the condition of expression(7).

FIG. 14 illustrates optical admittances of the lower layers 11 inEmbodiments 8 to 64 for an incident wavelength λ=900 nm in the complexcoordinate system. The upper limit of the condition of expression (8) isillustrated by a dashed-dotted line circle. As understood from FIG. 14,the optical admittances of the lower layers 11 in Embodiments 8 to 64for λ=900 nm satisfy the condition of expression (8).

FIG. 15 illustrates optical admittances of the lower layers 11 inEmbodiments 8 to 64 for an incident wavelength λ=1800 nm in the complexcoordinate system. The upper limit of the condition of expression (9) isillustrated by a long broken line circle. As understood from FIG. 15,the optical admittances of the lower layers 11 in Embodiments 8 to 64for λ=1800 nm satisfy the condition of expression (9).

FIG. 16 illustrates reflectances in the wavelength range from 430 to1800 nm for an incident angle of 0 degree in Embodiments 8 to 64. Asunderstood from FIG. 16, all of the reflectances in the wavelength rangefrom 430 to 1800 nm are 1.5% or less, which provides an extremely highantireflection performance.

FIG. 17 illustrates reflectances in the wavelength range from 430 to1800 nm for an incident angle of 45 degrees in Embodiments 8 to 64. Asunderstood from FIG. 17, all of the reflectances in the wavelength rangefrom 430 to 1800 nm are 4.5% or less, which provides a highantireflection performance.

TABLE 2 Refractive Embodiment Layer Material index 8 9 10 11 12 13 1412th Hollow 1.25 Physical 145.0 145.0 145.0 145.0 145.0 145.0 145.0 SiO₂Film 11th Ta₂O₅ 2.30 Thickness 5.0 5.0 5.0 5.0 5.0 5.0 5.0 10th SiO₂1.46 (nm) 130.1 128.0 122.2 117.8 116.9 115.5 112.7 9th Ta₂O₅ 2.30 20.621.4 21.5 23.4 22.3 22.5 22.7 8th SiO₂ 1.46 67.2 64.5 61.3 55.3 56.054.2 51.4 7th Ta₂O₅ 2.30 32.4 35.1 37.7 42.8 41.9 42.9 44.3 6th SiO₂1.46 58.6 52.8 47.1 37.6 36.4 32.7 27.3 5th Ta₂O₅ 2.30 31.9 37.3 42.351.8 53.0 57.4 63.7 4th SiO₂ 1.46 69.3 59.1 48.8 35.3 31.4 24.6 16.2 3rdTa₂O₅ 2.30 22.3 29.1 35.0 44.8 48.2 55.2 65.3 2nd SiO₂ 1.46 85.5 66.551.3 38.4 30.8 22.7 14.3 1st Ta₂O₅ 2.30 8.8 12.5 15.4 20.1 21.9 25.330.2 Substrate Refractive 1.50 1.60 1.70 1.80 1.90 2.00 2.10 index

TABLE 3 Refractive Embodiment Layer Material index 15 16 17 18 19 20 21Upper- Hollow 1.25 Physical 145.0 145.0 145.0 145.0 145.0 145.0 145.0most SiO₂ Film 16th Ta₂O₅ 2.30 Thickness 1.8 15th SiO₂ 1.46 (nm) 15.021.6 14th Ta₂O₅ 2.30 7.5 7.8 6.4 13th SiO₂ 1.46 6.3 86.7 83.4 76.7 12thTa₂O₅ 2.30 3.4 23.0 27.8 27.9 11th SiO₂ 1.46 130.5 98.3 39.3 35.8 35.110th Ta₂O₅ 2.30 5.7 18.3 19.6 43.6 50.4 49.0 9th SiO₂ 1.46 153.6 118.242.0 39.6 16.2 10.1 9.4 8th Ta₂O₅ 2.30 16.0 21.3 38.2 37.2 71.3 111.1118.8 7th SiO₂ 1.46 68.7 60.7 15.7 14.6 8.6 7.8 7.5 6th Ta₂O₅ 2.30 27.434.3 160.3 159.5 61.5 56.2 54.2 5th SiO₂ 1.46 58.1 48.7 12.6 14.3 20.425.3 25.3 4th Ta₂O₅ 2.30 28.7 35.6 39.4 39.5 39.6 38.6 37.8 3rd SiO₂1.46 54.8 52.2 31.5 33.4 39.1 42.8 43.0 2nd Ta₂O₅ 2.30 16.0 20.2 18.919.6 18.4 17.8 17.4 1st Al₂O₃ 1.63 142.7 148.9 108.7 112.9 118.5 132.4131.3 Substrate Refractive 1.50 1.50 1.50 1.50 1.50 1.50 1.50 index

TABLE 4 Refractive Embodiment Layer Material index 22 23 24 25 26 27 28Upper- Hollow 1.25 Physical 145.0 145.0 145.0 145.0 145.0 145.0 145.0most SiO₂ Film 16th Ta₂O₅ 2.30 Thickness 5.0 15th SiO₂ 1.46 (nm) 28.649.4 14th Ta₂O₅ 2.30 5.0 5.0 3.6 13th SiO₂ 1.46 29.1 54.4 87.4 54.2 12thTa₂O₅ 2.30 5.0 3.9 22.5 23.5 11th SiO₂ 1.46 130.2 88.4 51.8 20.6 16.510th Ta₂O₅ 2.30 5.0 19.0 26.4 26.3 7.7 5.0 9th SiO₂ 1.46 175.8 136.742.4 40.4 37.2 22.3 22.1 8th Ta₂O₅ 2.30 14.3 19.3 39.4 48.2 47.5 46.746.6 7th SiO₂ 1.46 69.0 61.9 14.9 13.5 12.4 12.7 11.8 6th Ta₂O₅ 2.3029.7 34.1 172.4 195.7 194.8 197.0 194.3 5th SiO₂ 1.46 53.3 42.3 7.4 8.98.4 8.5 8.3 4th Ta₂O₅ 2.30 41.0 44.8 47.1 56.6 57.9 56.3 57.4 3rd SiO₂1.46 33.8 28.3 11.4 16.4 15.8 16.0 15.7 2nd Ta₂O₅ 2.30 41.5 40.6 26.241.0 42.7 40.9 42.1 1st Al₂O₃ 1.63 20.2 12.6 2.9 10.0 10.0 10.0 10.0Substrate Refractive 2.10 2.10 2.10 2.10 2.10 2.10 2.10 index

TABLE 5 Refractive Embodiment Layer Material index 29 30 31 32 33 34 35Upper- Hollow 1.25 Physical 145.0 145.0 145.0 145.0 145.0 145.0 145.0most SiO₂ Film 16th Ta₂O₅ 2.30 Thickness 17.5 15th SiO₂ 1.46 (nm) 2.77.5 14th Ta₂O₅ 2.30 40.9 36.9 67.5 13th SiO₂ 1.46 5.0 6.4 7.5 9.9 12thTa₂O₅ 2.30 130.1 112.3 84.1 64.3 19.6 11th SiO₂ 1.46 4.9 24.6 30.7 31.020.6 10th Ta₂O₅ 2.30 150.1 41.8 49.5 44.4 25.3 15.0 9th SiO₂ 1.46 17.615.4 48.8 55.4 28.6 17.2 8th Ta₂O₅ 2.30 166.5 70.0 66.1 30.8 28.5 4.111.4 7th SiO₂ 1.46 13.3 30.0 26.5 55.8 59.3 162.4 178.1 6th Ta₂O₅ 2.3080.2 63.1 67.7 37.7 37.9 19.8 19.8 5th SiO₂ 1.46 21.5 29.8 24.9 38.340.0 43.2 43.1 4th Ta₂O₅ 2.30 77.7 70.0 76.4 60.0 60.5 48.3 48.8 3rdSiO₂ 1.46 18.4 19.6 16.3 19.2 21.8 24.4 24.5 2nd Ta₂O₅ 2.30 81.6 80.083.7 75.3 78.5 71.6 72.7 1st Al₂O₃ 1.63 10.0 6.8 6.2 5.0 7.4 8.5 8.4Substrate Refractive 1.50 1.50 1.50 1.50 1.50 1.50 1.50 index

TABLE 6 Refractive Embodiment Layer Material index 36 37 38 39 40 41 4243 Upper- Hollow 1.25 Physical 145.0 145.0 145.0 145.0 145.0 145.0 145.0145.0 most SiO₂ Film 16th SiO₂ 1.46 Thickness 25.4 15th Ta₂O₅ 2.30 (nm)5.0 5.9 14th SiO₂ 1.46 34.6 67.6 82.2 13th Ta₂O₅ 2.30 5.0 5.2 5.9 15.412th SiO₂ 1.46 130.1 110.5 85.4 44.0 17.3 11th Ta₂O₅ 2.30 5.8 22.2 28.625.7 16.5 10th SiO₂ 1.46 149.4 35.5 51.2 41.2 36.6 29.5 9th Ta₂O₅ 2.306.7 18.1 16.1 43.7 52.5 48.2 47.6 8th SiO₂ 1.46 156.6 124.2 62.3 53.027.5 15.3 15.1 11.7 7th Ta₂O₅ 2.30 17.0 20.9 34.9 34.0 62.3 87.4 77.5180.1 6th SiO₂ 1.46 65.5 54.5 43.0 39.0 16.1 5.0 5.0 3.8 5th Ta₂O₅ 2.3032.9 34.1 45.4 43.9 63.2 82.6 80.6 39.3 4th SiO₂ 1.46 43.3 36.5 29.125.5 13.7 9.8 8.3 7.3 3rd Ta₂O₅ 2.30 40.6 41.9 41.8 38.2 30.6 56.8 54.642.5 2nd SiO₂ 1.46 20.9 16.3 11.6 9.7 2.3 12.9 11.5 11.4 1st Ta₂O₅ 2.305.0 5.0 3.3 5.0 5.0 24.2 23.8 21.7 Substrate Refractive 2.10 2.10 2.102.10 2.10 2.10 2.10 2.10 index

TABLE 7 Refractive Embodiment Layer Material index 44 45 46 47 48 49 5051 13th Hollow 1.25 Physical 105.0 130.0 160.0 190.0 105.0 130.0 160.0190.0 SiO₂ Film 12th Ta₂O₅ 2.30 Thickness 3.3 6.8 6.3 6.6 3.0 5.0 5.05.7 11th SiO₂ 1.46 (nm) 93.5 81.4 91.7 100.6 111.9 103.6 111.6 103.410th Ta₂O₅ 2.30 17.8 19.8 23.0 28.9 20.0 22.7 23.2 26.2 9th SiO₂ 1.4639.0 34.6 36.5 41.0 45.8 43.3 46.4 44.2 8th Ta₂O₅ 2.30 35.7 35.2 40.757.1 41.5 44.0 46.1 47.5 7th SiO₂ 1.46 14.6 13.0 10.4 17.7 17.8 15.316.4 17.8 6th Ta₂O₅ 2.30 165.1 163.6 139.9 80.3 188.9 189.1 199.9 188.55th SiO₂ 1.46 14.7 15.1 11.8 16.9 9.3 7.9 8.6 13.8 4th Ta₂O₅ 2.30 41.742.1 41.3 56.0 57.3 54.6 56.7 51.3 3rd SiO₂ 1.46 35.0 35.5 32.2 34.416.7 13.8 14.2 21.6 2nd Ta₂O₅ 2.30 20.1 20.9 20.9 25.5 41.2 35.9 34.838.8 1st Al₂O₃ 1.63 117.1 129.1 109.0 116.2 9.7 6.0 5.0 12.1 SubstrateRefractive 1.50 1.50 1.50 1.50 2.10 2.10 2.10 2.10 index

TABLE 8 Refractive Embodiment Layer Material index 52 53 54 55 56 5713th Hollow 1.25 Physical 105.0 130.0 160.0 105.0 130.0 160.0 SiO₂ Film12th SiO₂ 1.46 Thickness 130.1 145.5 154.9 119.8 119.8 132.2 11th Ta₂O₅2.30 (nm) 16.7 16.1 17.9 6.7 11.7 7.6 10th SiO₂ 1.46 56.9 66.7 68.6 28.051.4 23.9 9th Ta₂O₅ 2.30 35.6 29.2 31.5 15.7 28.7 15.9 8th SiO₂ 1.4641.8 57.3 59.9 43.0 36.7 47.1 7th Ta₂O₅ 2.30 45.5 32.0 31.9 38.8 49.739.6 6th SiO₂ 1.46 43.3 62.0 67.3 27.5 21.0 31.4 5th Ta₂O₅ 2.30 38.324.8 22.5 59.4 67.1 55.4 4th SiO₂ 1.46 59.2 75.5 82.3 15.7 13.3 18.3 3rdTa₂O₅ 2.30 22.9 14.6 12.0 65.3 65.1 57.8 2nd SiO₂ 1.46 75.9 82.7 84.313.4 13.0 13.3 1st Ta₂O₅ 2.30 8.6 5.0 3.3 33.1 33.1 26.0 SubstrateRefractive 1.50 1.50 1.50 2.10 2.10 2.10 index

TABLE 9 Refractive Embodiment Layer Material index 58 59 60 61 13thHollow Refractive 1.10 1.29 1.10 1.29 SiO₂ index Film 172.8 151.0 175.9157.6 Thickness (nm) 12th Ta₂O₅ 2.30 Physical 5.0 12.0 2.5 10.7 11thSiO₂ 1.46 Film 113.2 66.3 132.3 80.8 10th Ta₂O₅ 2.30 Thickness 21.2 23.720.1 28.1 9th SiO₂ 1.46 (nm) 43.9 24.6 51.5 36.1 8th Ta₂O₅ 2.30 40.531.1 42.8 47.0 7th SiO₂ 1.46 12.0 10.4 18.7 11.8 6th Ta₂O₅ 2.30 148.9168.7 194.2 181.9 5th SiO₂ 1.46 13.5 17.2 8.3 7.0 4th Ta₂O₅ 2.30 43.643.2 60.0 52.1 3rd SiO₂ 1.46 35.8 38.2 15.9 14.1 2nd Ta₂O₅ 2.30 21.720.3 41.1 40.1 1st Al₂O₃ 1.63 126.0 123.8 10.0 9.8 Substrate Refractive1.50 1.50 2.10 2.10 index

TABLE 10 Refractive Embodiment Layer Material index 62 63 64 13th HollowRefractive 1.29 1.10 1.29 SiO₂ index Film 148.0 155.5 143.7 Thickness(nm) 12th SiO₂ 1.46 Physical 151.5 130.0 128.3 11th Ta₂O₅ 2.30 Film 5.04.5 5.5 10th SiO₂ 1.46 Thickness 25.4 57.8 47.2 9th Ta₂O₅ 2.30 (nm) 8.413.9 16.1 8th SiO₂ 1.46 75.0 56.3 57.1 7th Ta₂O₅ 2.30 18.6 31.7 31.9 6thSiO₂ 1.46 80.0 42.9 43.1 5th Ta₂O₅ 2.30 17.3 42.8 42.5 4th SiO₂ 1.4686.2 28.9 28.4 3rd Ta₂O₅ 2.30 11.3 41.2 39.5 2nd SiO₂ 1.46 85.3 12.811.7 1st Ta₂O₅ 2.30 4.0 5.0 5.0 Substrate Refractive 1.50 2.10 2.10index

Embodiment 65

FIG. 18 illustrates a surveillance network camera 200 as an opticalapparatus that is Embodiment 65 of the present invention. The camera 200includes an image capturing optical system 201 that forms an opticalimage of an object and a main body (holder) 202 that holds the imagecapturing optical system 201. The image capturing optical system 201 isconstituted by multiple lenses.

On a surface of at least one lens (optical element) among these lenses,the antireflection coating 10 of any one of Embodiments 1 to 64 isformed.

Forming the antireflection coating on the lens enables the camera 200not only to produce an image in which a generation of unwanted lightsuch as flare and ghost is reduced, but also to increase an amount oftransmitted light so as to obtain more image information, which achievesa high performance camera.

Although this embodiment described the network camera as an example ofoptical apparatuses, the antireflection coatings of Embodiments 1 to 64can be formed on an optical element included in various opticalapparatuses other than the network camera, such as image capturingapparatuses and interchangeable lenses.

Each of the above-described embodiments can provide an antireflectioncoating having a high antireflection performance in a wide wavelengthrange from 430 nm to 1800 nm in which visible light and airglow can beused. Furthermore, using an optical element provided with thisantireflection coating enables achieving an optical system and anoptical apparatus each having a high optical performance.

Although this embodiment described the camera as an example of opticalapparatuses, the optical apparatuses include an interchangeable lensthat includes an image capturing optical system (including an opticalelement on which the antireflection coating of any one of Embodiments 1to 64 is formed) and a lens barrel as a holding member holding the imagecapturing optical system.

While the present invention has been described with reference toexemplary embodiments, it is to be understood that the invention is notlimited to the disclosed exemplary embodiments. The scope of thefollowing claims is to be accorded the broadest interpretation so as toencompass all such modifications and equivalent structures andfunctions.

This application claims the benefit of Japanese Patent Application No.2015-204574, filed on Oct. 16, 2015, which is hereby incorporated byreference herein in its entirety.

What is claimed is:
 1. An antireflection coating as a multi-layer filmto be formed on a surface of a substrate, the antireflection coatingcomprising: multiple layers including: an uppermost layer most distantfrom the substrate among the multiple layers; and a lower layerincluding at least one layer other than the uppermost layer, wherein: arefractive index n_(m) of the uppermost layer for a wavelength of λ (nm)satisfies the following condition:1.1≤n _(m)≤1.3; and an optical admittance Y of the lower layer isexpressed by Y=a+ib, and a and b in the optical admittance satisfy thefollowing conditions:(a−1.13)²+(b−0.24)²≤0.45² for λ=430;(a−1.33)²+(b+0.05)²≤0.25² for λ=900; and(a−1.14)²+(b+0.25)²≤0.29² for λ=1800; and wherein: when an incidentangle of a ray, whose wavelength λ (nm) is in a range of 430≤λ≤1800, tothe antireflection coating is 0° or more and 15° or less, a reflectanceof the antireflection coating is 1.5% or less; and when the incidentangle of the ray is 30° or more and 45° or less, the reflectance of theantireflection coating is 4.5% or less.
 2. The antireflection coatingaccording to claim 1, wherein a and b in the optical admittance satisfythe following conditions:(a−1.10)²+(b−0.22)²≤0.26² for λ=430;(a−1.33)²+(b+0.05)²≤0.20² for λ=900; and(a−1.18)²+(b+0.26)²≤0.25² for λ=1800.
 3. The antireflection coatingaccording to claim 1, wherein a and b in the optical admittance satisfyat least one of the following conditions in a wavelength range of430≤λ≤1800:(a−1.09)²+(b−0.20)²≤0.35²;(a−1.28)² +b ²≤0.35²; and(a−1.27)²+(b+0.28)²≤0.35².
 4. The antireflection coating according toclaim 1, wherein a film thickness d_(m) (nm) of the uppermost layersatisfies the following condition:125≤n _(m) ×d _(m)≤250.
 5. The antireflection coating according to claim1, wherein the multiple layers includes nine or more layers.
 6. Theantireflection coating according to claim 1, wherein when, amongmaterials of two or more layers of the lower layer, a highest refractiveindex material has a refractive index represented by n_(H), and a lowestrefractive index material has a refractive index represented by n_(L),n_(H) and n_(L) satisfy the following condition:0.4≤n _(H) −n _(L)≤0.9.
 7. The antireflection coating according to claim1, wherein the uppermost layer is formed as a layer including a void. 8.The antireflection coating according to claim 1, wherein a material ofthe uppermost layer is oxide silicon or magnesium fluoride.
 9. Theantireflection coating according to claim 1, wherein the uppermost layeris a film formed by a sol-gel method.
 10. The antireflection coatingaccording to claim 1, wherein the lower layer is a film formed by avacuum evaporation method or a sputtering method.
 11. The antireflectioncoating according to claim 1, wherein a material of the lower layer isany one of oxides of titanium, tantalum, zirconia, chromium, niobium,cerium, hafnium, aluminium, silicon and yttrium, or a mixture thereof.12. An optical element comprising: an optical element body as asubstrate; and an antireflection coating as a multi-layer film formed ona surface of the optical element body, wherein the antireflectioncoating comprises: multiple layers including: an uppermost layer mostdistant from the substrate among the multiple layers; and a lower layerincluding at least one layer other than the uppermost layer, wherein: arefractive index n_(m) of the uppermost layer for a wavelength of λ (nm)satisfies the following condition:1.1≤n _(m)≤1.3; and an optical admittance Y of the lower layer isexpressed by Y=a+ib, and a and b in the optical admittance satisfy thefollowing conditions:(a−1.13)²+(b−0.24)²≤1.45² for λ=430;(a−1.33)²+(b+0.05)²≤1.25² for λ=900; and(a−1.14)²+(b+0.25)²≤1.29² for λ=1800; and wherein: when an incidentangle of a ray, whose wavelength λ (nm) is in a range of 430≤λ≤1800, tothe antireflection coating is 0° or more and 15° or less, a reflectanceof the antireflection coating is 1.5% or less; and when the incidentangle of the ray is 30° or more and 45° or less, the reflectance of theantireflection coating is 4.5% or less.
 13. An optical apparatuscomprising: an optical element; and a holder holding the opticalelement, wherein the optical element comprises: an optical element bodyas a substrate; and an antireflection coating as a multi-layer filmformed on a surface of the optical element body, wherein theantireflection coating comprises: multiple layers including: anuppermost layer most distant from the substrate among the multiplelayers; and a lower layer including at least one layer other than theuppermost layer, wherein: a refractive index n_(m) of the uppermostlayer for a wavelength of λ (nm) satisfies the following condition:1.1≤n _(m)≤1.3; and an optical admittance Y of the lower layer isexpressed by Y=a+ib, and a and b in the optical admittance satisfy thefollowing conditions:(a−1.13)²+(b−0.24)²≤1.45² for λ=430;(a−1.33)²+(b+0.05)²≤1.25² for λ=900; and(a−1.14)²+(b+0.25)²≤1.29² for λ=1800; and wherein: when an incidentangle of a ray, whose wavelength λ (nm) is in a range of 430≤λ≤1800, tothe antireflection coating is 0° or more and 15° or less, a reflectanceof the antireflection coating is 1.5% or less; and when the incidentangle of the ray is 30° or more and 45° or less, the reflectance of theantireflection coating is 4.5% or less.